"The call was transferred through to a ward, and a short conversation was held with one of the nursing staff," the hospital said in a statement. "King Edward VII's Hospital deeply regrets this incident."
The radio station also apologized for the prank call.
"2Day FM sincerely apologizes for any inconvenience caused by the inquiry to Kate's hospital. The radio segment was done with lighthearted intentions," the station said in a statement earlier.
DJs in Hiding
Greig and Christian are said to be in a fragile emotional state since Saldanha was found dead on Friday.
Station executives said the hosts are seeking the help of counselors.
"These people aren't machines, they're human beings," Holleran told reporters on Saturday. "We're all affected by this."
The DJs are in hiding and their Facebook and twitter accounts are now dark.
The Sydney radio station -- famous for its pranks and outrageousness -- has suspended all advertising in the face an advertising boycott and Greig and Christian have been pulled off the air.
Last spring, the station was warned by Australia's broadcast regulator about violations of the "decency provision" of the country's broadcast code.
Night Out Without Kate
Prince William was on his own Saturday night at a charity ball, for his first public function since his wife's pregnancy was announced.
In conversation he quipped about his Kate's illness: "I don't know why they call it morning sickness -- they should call it all day and all night sickness."
He did not talk about the tragic death of the nurse who fell victim to the hoax call, but he and Kate have issued a statement of sympathy for the family.
"The Duke and Duchess of Cambridge are deeply saddened to learn of the death of Jacintha Saldanha," a spokesman from St. James Palace said in a statement.
For Kate, it is yet another test of her new life as a very public royal. In September, a tabloid photographer using an extremely long lens photographed her topless on a private vacation.
"While she understood what she was taking on, there have been a couple of things that will have made them go oh my goodness and think we didn't think it would be that bad in this day and age," said Victoria Murphy, royal reporter with The Daily Mirror.
The Associated Press contributed to this report.